New implementation of high‐level correlated methods using a general block tensor library for high‐performance electronic structure calculations

Abstract

This article presents an open‐source object‐oriented C++ library of classes and routines to perform tensor algebra. The primary purpose of the library is to enable post‐Hartree–Fock electronic structure methods; however, the code is general enough to be applicable in other areas of physical and computational sciences. The library supports tensors of arbitrary order (dimensionality), size, and symmetry. Implemented data structures and algorithms operate on large tensors by splitting them into smaller blocks, storing them both in core memory and in files on disk, and applying divide‐and‐conquer‐type parallel algorithms to perform tensor algebra. The library offers a set of general tensor symmetry algorithms and a full implementation of tensor symmetries typically found in electronic structure theory: permutational, spin, and molecular point group symmetry. The Q‐Chem electronic structure software uses this library to drive coupled‐cluster, equation‐of‐motion, and algebraic‐diagrammatic construction methods. © 2013 Wiley Periodicals, Inc.

Combining Internally Contracted States and Matrix Product States To Perform Multireference Perturbation Theory

“…114 Several computer libraries capable of efficiently evaluating the final sequence of binary contractions have recently become available. [70][71][72][73] We here use a prototyping library developed by one us, which will be described elsewhere.…”

A General Sparse Tensor Framework for Electronic Structure Theory

“…17 While the focus of this work is on the exploitation of small-5 block sparsity such as that found in the two-electron integral tensor, the algorithms discussed herein can also be used to treat more structured sparsity through appropriate block definition.…”

“…In order to obtain high floating point efficiency through the use of existing highly optimized matrix multiply routines, our library stores tensors using the well-established "block-major order." 12,17,26,28 In order to give a clear definition of "block-major order," we wish to clarify several terms. Throughout this document, we will use the terms "index" and "subspace" somewhat interchangeably.…”

“…13,14 The TCE has been used to implement extremely complex electronic structure methods, with a particular emphasis on high-order coupled cluster methods. 13,15,16 In an alternate line of development, Epifanovsky et al have developed the libtensor project, a high-level symbolic C++ library to describe block tensor operations, 17 , following an early implementation of the C++ block-tensor library powering coupled-cluster methods in Q- In this work, we shall describe our block-sparse tensor library, an extension of the libtensor project. 17 We shall provide the first detailed description of an implementation capable of handling fully-general multi-dimensional sparsity in tensor contractions.…”

“…13,15,16 In an alternate line of development, Epifanovsky et al have developed the libtensor project, a high-level symbolic C++ library to describe block tensor operations, 17 , following an early implementation of the C++ block-tensor library powering coupled-cluster methods in Q- In this work, we shall describe our block-sparse tensor library, an extension of the libtensor project. 17 We shall provide the first detailed description of an implementation capable of handling fully-general multi-dimensional sparsity in tensor contractions. Our library has the unique ability to represent universally sparse contractions, in which the output and all input tensors have uniquely defined sparse structures.…”